Random particle methods applied to broadband fan interaction noise

Predicting broadband fan noise is key to reduce noise emissions from aircraft and wind turbines. Complete CFD simulations of broadband fan noise generation remain too expensive to be used routinely for engineering design. A more efficient approach consists in synthesizing a turbulent velocity field that captures the main features of the exact solution. This synthetic turbulence is then used in a noise source model. This paper concentrates on predicting broadband fan noise interaction (also called leading edge noise) and demonstrates that a random particle mesh method (RPM) is well suited for simulating this source mechanism. The linearized Euler equations are used to describe sound generation and propagation. In this work, the definition of the filter kernel is generalized to include non-Gaussian filters that can directly follow more realistic energy spectra such as the ones developed by Liepmann and von Kármán. The velocity correlation and energy spectrum of the turbulence are found to be well captured by the RPM. The acoustic predictions are successfully validated against Amiet’s analytical solution for a flat plate in a turbulent stream. A standard Langevin equation is used to model temporal decorrelation, but the presence of numerical issues leads to the introduction and validation of a second-order Langevin model.     

Sound radiation from point acoustic stresses in circular motion

The general result for the sound field of a point acoustic stress in arbitrary motion is applied in this paper to study the effects of (i) uniform straight-line motion, (ii) uniform circular motion and (iii) pure rotation on the overall sound radiation from random point acoustic stresses. The effects of acceleration of the stresses due to steady rotation in a circle are established, using the moving-source approach adopted in two previous papers for the far-field sound radiation from rotating point forces and point sources. Applications include the turbulent sound generation from tip jet rotors and noise from rotating blades with distributed forces.     

快速随机粒子网格法的气动噪声预测方法

耦合随机湍流速度生成模型与线化欧拉方程技术,形成了一套具备模拟噪声在非均匀流场中传播能力的气动噪声混合预测方法。该混合方法的随机湍流速度生成模型采用了快速随机粒子网格法,为声传播模拟提供了可靠的源项。而噪声的传播计算选用线化欧拉方程,其空间离散采用9点5阶的色散保持关系格式,时间推进选用了高精度大时间步长的6级4阶龙格库塔格式,远场边界应用了无分裂形式的理想匹配层边界条件。首先,选用高斯脉冲传播算例对线化欧拉方程的时空离散格式、远场无反射边界条件进行了验证分析。然后,计算分析各向同性湍流的空间相关性验证湍流速度生成模型的可靠性。最后,基于已搭建的气动噪声混合预测方法进行了30P30N三段翼缝翼噪声的计算分析。计算分析可知:监测点处功率谱密度曲线、噪声指向性等计算结果与参考文献结果取得了较好的一致性。数值计算结果表明所建立的气动噪声混合预测方法能有效预测二维复杂构型的气动噪声问题。      

An investigation into the noise generation of CPAP devices: Experimental and numerical study

Continuous positive airway pressure (CPAP) devices are popularly used for obstructive sleep apnoea (OSA) treatment. However, the noise level emission from these devices has been identified as a potential factor for patient’s discomfort and rejection. There is a need to obtain information on the noise characteristics and source locations in order to tackle the most serious noise source within these devices. A typical CPAP device was used for the investigation and its sound characteristics and sound power levels were determined. The noise generated from a centrifugal fan was also independently investigated to address its contribution to the overall noise of the device. Frequency analysis suggested that the noise generated from both the CPAP device and the fan is broadband in nature with discrete peaks containing rotational and non-rotational components. The broadband components were then studied in detail using numerical simulation approach. Computational aeroacoustics (CAA) method with hybrid approach was used to a three-dimensional (3-D) CPAP fluid model to predict the aerodynamic and aeroacoustics behaviours of the device. This showed a complicated flow structure involving flow separation, rotation, and vortices in several locations which resulted in high level of flow turbulence inside the device. The turbulent components were used to estimate the broadband noise level at source using the broadband noise source (BNS) models. It shows the most critical location is at the fan region and at the fan inlet.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Coherence function and mean field of plane and spherical sound waves propagating through inhomogeneous anisotropic turbulence

Inhomogeneity and anisotropy are intrinsic characteristics of daytime and nighttime atmospheric turbulence. For example, turbulent eddies are often stretched in the direction of the mean wind, and the turbulence statistics depends on the height above the ground. Recent studies have shown that the log-amplitude and phase fluctuations of plane and spherical sound waves are significantly affected by turbulence inhomogeneity and anisotropy. The present paper is devoted to studies of the mean sound field and the coherence functions of plane and spherical sound waves propagating through inhomogeneous anisotropic turbulence with temperature and velocity fluctuations. These statistical moments of a sound field are important in many practical applications, e.g., for source detection, ranging, and recognition. Formulas are derived for the mean sound field and coherence function of initially arbitrary waveform. Using the latter formula, we also obtained formulas for the coherence functions of plane and spherical sound waves. All these formulas coincide with those known in the literature for two limiting cases: homogeneous isotropic turbulence with temperature and wind velocity fluctuations, and inhomogeneous anisotropic turbulence with temperature fluctuations only. Using the formulas obtained, we have numerically shown that turbulence inhomogeneity significantly affects the coherence functions of plane and spherical sound waves.     

Injection and mixing in a scramjet combustor: DES and RANS studies

The low momentum flux ratio jet in the HyShot II scramjet combustor is studied by DES (Detached Eddy Simulation) and RANS (Reynolds-Averaged Navier–Stokes) methods. The flow structure near the injector, shock pattern in the symmetry plane as well as the instantaneous coherent structures are presented and explained. Further insight into the flow physics is obtained by visualizing instantaneous coherent structures. The formation of Ω-shaped vortices, which was previously observed in experiments but never well-studied numerically, is discussed in detail. A new schematic of flow physics is proposed to enhance the understanding of the low momentum flux ratio jet. Compared to the DES result, the RANS method is unable to capture the dynamics of turbulent structures. The DES method provides much detailed information about mixing patterns and a more reliable mixing efficiency than the RANS result. The RANS method over-predicts the eddy-viscosity during turbulence modeling and suppresses unsteady turbulent fluctuations by time averaging, which results in a 25% over-estimation of the mixing efficiency.     

Sound-wave coherence in atmospheric turbulence with intrinsic and global intermittency

The coherence function of sound waves propagating through an intermittently turbulent atmosphere is calculated theoretically. Intermittency mechanisms due to both the turbulent energy cascade (intrinsic intermittency) and spatially uneven production (global intermittency) are modeled using ensembles of quasiwavelets (QWs), which are analogous to turbulent eddies. The intrinsic intermittency is associated with decreasing spatial density (packing fraction) of the QWs with decreasing size. Global intermittency is introduced by allowing the local strength of the turbulence, as manifested by the amplitudes of the QWs, to vary in space according to superimposed Markov processes. The resulting turbulence spectrum is then used to evaluate the coherence function of a plane sound wave undergoing line-of-sight propagation. Predictions are made by a general simulation method and by an analytical derivation valid in the limit of Gaussian fluctuations in signal phase. It is shown that the average coherence function increases as a result of both intrinsic and global intermittency. When global intermittency is very strong, signal phase fluctuations become highly non-Gaussian and the average coherence is dominated by episodes with weak turbulence.     

三维FW-H方程与CAA数值模拟匹配技术研究

本文研究了三维FW-H方程与CAA数值模拟匹配技术。首先验证了适于亚音任意运动声源的Farassat时域公式和适于亚音匀速直线运动声源的Lockard频域公式,采用均匀流中单极子源声辐射问题对两类公式进行了校核。进一步,采用FW-H／CAA匹配技术对风扇／压气机前传声进行了预测。近声场基于轴对称三维CAA方法获得,远声场则基于近声场数据采用三维可穿透FW-H方程时域公式进行预测,并校核算例着重分析了不同积分面对远场声指向性的影响。本文研究证实了FW-H／CAA数值模拟匹配技术的可行性和解决工程实际问题的潜力。     

Statistics of a coherent lidar signal in a turbulent atmosphere

Absolute and conditional statistical properties of a pulse coherent Doppler lidar signal in a turbulent atmosphere are studied. Upon coherent receiving of optical fields scattered by a large number of particles, the lidar signal is shown to be a nonstationary non-Gaussian random process with Gaussian conditional statistical characteristics. The appearance of non-Gaussian properties of the signal is caused by correlation of turbulent fluctuations of the wind velocity field within the scattering volume. For the considered signal model, which corresponds to the single scattering approximation and is a sum of a large number of random variables, the central limit theorem is found to be untrue due to the statistical dependence of particles’ positions in a turbulent atmosphere. The results of numerical calculations show that, for a homogeneous and isotropic turbulence, the behavior of the signal statistics significantly depends on the size of the scattering volume and on the state of atmospheric turbulence. A Gaussian statistics is observed at small heights; with an increase in height, the non-Gaussian component becomes considerable in fluctuations of the lidar signal.     

共轴双旋翼悬停状态气动噪声特性分析

结合CFD(Computational fluid dynamics)方法和FW-H(Ffowcs Williams-Hawkings)方程,建立了一套适合于悬停状态下共轴刚性双旋翼气动噪声特性计算方法。为了准确模拟共轴旋翼流场的涡干扰现象和非定常特性,基于运动嵌套网格技术与双时间推进方法,采用积分形式的可压雷诺平均Navier-Stokes(RANS)方程作为双旋翼非定常流场求解控制方程,湍流模型选用Baldwin-Lomax模型。通过Farassat 1A公式计算双旋翼气动噪声特性,每个声源微面的位置和载荷信息直接从桨叶表面网格中获取。然后,对水平面内和竖直面内观测点处共轴双旋翼厚度噪声、载荷噪声和总噪声的声压时间历程和频谱特性做了细致对比。模拟结果表明:上旋翼和下旋翼反向旋转的特点对声压时间历程影响显著,不同方向观察点的声压波形峰值对应的相位不同;共轴旋翼流场中存在的文丘里效应、桨-涡干扰现象以及下洗流的作用使得桨叶气动载荷呈现明显的非定常特征,导致共轴双旋翼的载荷噪声辐射强度较大;在低频段,总噪声受厚度噪声主导,而在高频段则受载荷噪声主导。      

NOISE GENERATED BY A COANDA WALL JET CIRCULATION CONTROL DEVICE

An analysis is made of the production of sound by a hydrofoil with a Coanda wall jet circulation control (CC-) device. Three principal sources are identified in the vicinity of the trailing edge of the hydrofoil. The radiation at very low frequencies is dominated by “curvature noise” generated by the interaction of boundary layer turbulence with the rounded trailing edge of the CC-hydrofoil; this is similar in character and magnitude to the low-frequency component of the conventional trailing edge noise produced by a hydrofoil of the same chord, but with a sharp trailing edge. Higher frequency sound is produced principally at the Coanda jet slot. “Passive slot noise” is caused by the “scattering” by the slot lip of nearfield pressure fluctuations in the turbulent boundary layer of the exterior mean flow past the slot. This is of comparable intensity to high frequency, sharp-edged trailing edge noise. However, the acoustic spectrum is greatly extended to much higher frequencies if the Coanda jet is turbulent; the sound produced by the interaction of this turbulence with the lip tends to dominate the spectrum at frequencies f (Hz) greater than about U_j/h, where h is the slot width and U_jthe Coanda jet speed. Sample numerical results are presented for a typical underwater application that indicate that at this and higher frequencies the slot noise can be 20 dB or more greater than conventional trailing edge noise, although the differences become smaller as the thickness of the slot lip increases.     

Experimental investigation of the travel-time variance of an acoustic wave propagating through the grid-generated turbulence

An experimental technique for the investigation of the behaviour of acoustic wave propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. Travel-time variance is studied versus mean flow velocity, travel distance and outer turbulence scale. The effect of thermal fluctuations, which result in fluctuations of sound speed, is studied using a heated-grid experiment. Experimental data obtained using ultrasonic technique confirm numerical and theoretical predictions of nonlinear increase of the travel-time variance with propagation distance, which could be connected to the occurrence of caustics. The effect of turbulent intensity on the travel-time variance and appearance of caustics is studied. It is demonstrated experimentally that the higher turbulence intensity leads to the shorter distance, at which the first caustic occurs. The probability density for caustics appearance is analysed against the measured wave amplitude fluctuations. The analysis reveals that the region of high-amplitude fluctuations corresponds to the region where the probability of formation of random caustics differs from zero. Experimental results are in very good agreement with theoretical and numerical predictions.     

Fluctuations of spherical waves in a turbulent atmosphere: effect of the axisymmetric approximation in computational methods

The validity of the axisymmetric parabolic-equation (PE) method for line-of-sight sound propagation in a turbulent atmosphere is investigated. The axisymmetric PE method is a finite-difference method for solving a 2D parabolic wave equation, which follows from the 3D wave equation by the assumption of axial symmetry around the vertical axis through the source. It is found that this axisymmetric approximation has a considerable spurious effect on the fluctuations of the sound field. This is concluded from analytical expressions for the log-amplitude and phase variances, derived both for isotropic turbulence and for axisymmetric turbulence. The expressions for axisymmetric turbulence are compared with the results of numerical computations with the PE method.     

Long time correlations in lagrangian dynamics: a key to intermittency in turbulence

Using a new experimental technique, based on the scattering of ultrasounds, we perform a direct measurement of particle velocities, in a fully turbulent flow. This allows us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that is extremely long range correlated in time. Theoretically, a Langevin equation is proposed and shown to account for the observed one- and two-point statistics. This approach connects intermittency to the dynamics of the flow.     

Noise of a model helicopter rotor due to ingestion of isotropic turbulence

A theoretical and experimental investigation of the noise of a model helicopter rotor due to the ingestion of grid-generated, isotropic turbulence is described. Simulated forward flight and vertical ascent tests were performed with a 0·76 m diameter, articulated model rotor in the United Technologies Research Center Acoustic Research Tunnel. Far field noise spectra and directivity were measured in addition to inflow turbulence intensities, length scales and spectra. Measured inflow turbulence statistics and rotor operating parameters were employed in a theoretical procedure to predict turbulence ingestion noise spectra and directivity. This theoretical formulation represented an absolute level prediction method in that empirical or adjustable constants were not employed. From this study it is concluded that incident turbulence represents a potentially important source of rotor narrowband random (quasi-tonal) and broadband noise. With due regard to the absolute level nature of the prediction method, agreement between theory and experiment is reasonable: quasi-tonal noise at low frequency tends to be overpredicted whereas mid-frequency tonal noise and high frequency broadband noise are well predicted. This theory, therefore, provides a means to predict the contribution of turbulence ingestion noise to overall rotor noise spectra and directivity in cases where reasonable estimates of incident turbulence statistics can be made. Ingestion of main rotor wake turbulence by tail rotors in flight and ingestion of atmospheric turbulence by main and tail rotors in hover would be expected to be the most important sources of turbulence ingestion noise in full scale applications.     

Nature of inlet turbulence and strut flow disturbances and their effect on turbomachinery rotor noise

Results of an investigation in which turbomachinery rotor sound spectra were correlated with aerodynamic measurements of the inlet turbulence, strut wake, and vortex flow strengths are reported. Aerodynamic measurements included mean velocity profiles, turbulence intensity, and axial length scales. Inlet turbulence data indicate that the major effect of flow contraction appears to be the elongation of turbulent eddies. Eddies of this size dominate the blade passing frequency (BPF) tones. Decreasing eddy size by use of a grid revealed vortex flow strength to be the second major sound source. A doubling of vortex flow strength produced a 6 dB increase in the SPL of the first BPF. The sound pressure level showed less than a 2 dB change with doubling of strut wake turbulence intensity or velocity defect. A discussion of the relative importance of various sources of noise due to flow non-uniformities at the inlet is given.     

The prediction of jet noise ground effects using an acoustic analogy and a tailored Green's function

An assessment of an acoustic analogy for the mixing noise component of jet noise in the presence of an infinite surface is presented. The reflection of jet noise by the ground changes the distribution of acoustic energy and is characterized by constructive and destructive interference patterns. The equivalent sources are modeled based on the two-point cross-correlation of the turbulent velocity fluctuations and a steady Reynolds-Averaged Navier–Stokes (RANS) solution. Propagation effects, due to reflection by the surface and refraction by the jet shear layer, are taken into account by calculating the vector Green's function of the linearized Euler equations (LEE). The vector Green's function of the LEE is written in relation to that of Lilley's equation; that is, it is approximated with matched asymptotic solutions and Green's function of the convective Helmholtz equation. The Green's function of the convective Helmholtz equation in the presence of an infinite flat plane with impedance is the Weyl–van der Pol equation. Predictions are compared with measurements from an unheated Mach 0.95 jet. Microphones are placed at various heights and distances from the nozzle exit in the peak jet noise direction above an acoustically hard and an asphalt surface. The predictions are shown to accurately capture jet noise ground effects that are characterized by constructive and destructive interference patterns in the mid- and far-field and capture overall trends in the near-field.     

Time- and frequency-domain computations of broadband noise due to interaction between incident turbulence and rectilinear cascade of flat plates

Time-domain computational aeroacoustic (CAA) techniques are developed to investigate the broadband noise resulting from the interaction of a rectilinear cascade of flat plates with incident homogeneous, isotropic turbulence. The investigation is carried out by comparing the prediction results obtained by employing the time-domain CAA method with those using existing frequency-domain methods. A semi-analytic model (Wei & Cheong, 2010) and a full three-dimensional rectilinear cascade model (Lloyd & Peake, 2008; Lloyd, 2009) are adopted for the frequency-domain computations. By comparing these computation results, the three-dimensional characteristics of inflow turbulence noise are investigated; in particular, the effects of the wavenumber components of ingested turbulence in the spanwise direction are taken into consideration in the investigation. First, CAA results are compared with those from the semi-analytic model. The results for the acoustic modes of relatively low spanwise wavenumbers obtained using both methods show good agreement, but as the spanwise wavenumber increases, the results obtained by the two methods become increasingly different. To investigate in detail the reason for these differences, mode-decomposition analysis is performed by adopting a hybrid method as well as by employing the CAA and the semi-analytic method. The hybrid method involves the following two sequential computations: (i) the upwash velocities on the flat plate airfoils of the rectilinear cascade are first predicted using the frequency-domain method, and (ii) the acoustic wave propagation is subsequently analyzed using time-domain CAA techniques, with these upwash velocities applied as the boundary conditions on the flat plate. It is seen that the results of the time-domain CAA technique and the hybrid method show good agreement, irrespective of the wavenumber and frequency. However, comparisons of the acoustic solutions from three computations reveal that the prediction results of the semi-analytic model deviate more from the other two predictions as the spanwise wavenumber of the acoustic wave increases and the frequency decreases. On a basis of this observation, a formulation is derived for the error in the pressure jump across the flat-plate predicted by using the semi-analytic method. This formulation shows that the error is approximately inversely proportional to the sound speed in the spanwise direction of the concerned acoustic modes. This result quantitatively clarifies the limitations of applying the frequency-domain method of Wei & Cheong (2010) to the three-dimensional turbulence-cascade interaction problems. Secondly, the prediction results using the time-domain CAA method are compared with those from the full three-dimensional rectilinear model that is believed to be exact model for the cascade geometry considered in this paper. This comparison shows the good agreements between two predictions, which support the above arguments for the error and the successful application of the time-domain CAA methods. It is expected that these methods can be extended to the broadband noise problem in an annular cascade, including the nonlinear interaction of the real-airfoil cascade with the incident nonhomogeneous gust.